In the scene on a ice rink bench, Kris takes off the right shoe as if he is about to put the right ice skate on. While he talks with Vanessa, viewers can see his bended left knee, so he's actually putting the left one on. Then we see that his right shoe is magically back on his foot and he takes that shoe off once again and finally puts the right skate on.
At the family Christmas gathering, Richard introduces Vanessa to a third character as "my cousin, your second cousin." First cousins share the same grandparents, and second cousins share the same great-grandparents. Richard never refers to the third person as "my FIRST cousin". Working the quote backward, Vanessa's second cousin would be Richard's first cousin once removed, still referred to as a cousin.
Emilia's song was dubbed by a youth choir.
The family is supposedly watching the closing scene of It's a Wonderful Life (1946) (with the TV set offscreen) and the audience hears a chorus singing AULD LANG SYNE, with the last line as, "We'll take a cup of kindness yet, for the sake of auld lang syne." The now iconic actual closing scene uses the lyrics "We'll DRINK a cup of kindness yet, for--auld--lang syne," first with James Stewart's distinct voice standing out over the chorus, and then repeated with the ringing of the Liberty Bell of the short-lived Liberty Pictures logo.
Early in the movie, Richard is on a ladder hanging Christmas lights. He receives a text and falls off the ladder with a loud "thud". It sounds like he hit something hard, like compacted snow. However, when that sound happens he is just below the sight line, which is somewhere just around the middle of that ladder. For safety they probably had him land on something soft and added the noise in, but it was way too soon. The open vortex of the ladder shows that he had much further down to fall in reality if he went to the bottom of it.
In Act I, Richard is standing at the square in NYC (IRL it was Abbotsford, CA), and you can see several big green deciduous trees sprayed with faux snow in the week before Christmas! Movie was clearly shot in late April or May. They tried to cover it with a lot of stock footage which shows typical winter deciduous trees without leaves but there are more situation like this. In the front of Richard's house in Barrington, Connecticut, there are beautiful green deciduous shrubs sprayed with snow. When Vanessa and Chris get out of car in Richard's house front yard, you can see a lot of green and purple deciduous trees behind them with barely any snow on them. Around half of movie, Vanessa and Chris walk in the downtown, and you can see a lot of big beautiful green deciduous trees sprayed with barely any faux snow.
Vanessa brings one small suitcase on her trip to CT, but manages to wear 4 (FOUR) different full length winter coats and matching scarves. No way they would fit in that little suitcase.
The Christmas stockings show that the Hendricks' son's name is Aidan; the end credits list it as Aiden.